Abstract

Using GEPD data from Peru, this paper examines the psychometric properties of the mathematics portion of the teacher assessment module. We estimate a two parameter logistic (2PL) item response theory (IRT) model. We produce item characteristic curves (ICC) and test characteristic curves from this model. We then compare our results to data from a similar assessment used in the Service Delivery Indicators project in several Sub-Sahara African countries using an item equating approach.

Takeaways:

Methodological Approach

We use a model from Item Response Theory (IRT) to examine the functioning of the teacher knowledge test items for Language and Mathematics. The model used is the Two Parameter Logistic (2PL), which allows for items with binary responses (Correct/Incorrect) The model is as follows for item i and person j:

\[ P(u_{ij}=1|\theta_j,\omega)=\frac{exp(a_i(\theta_j - b_{i} ))}{1+exp(a_i(\theta_j - b_{i} ))} \]

Summary Statistics of Data

Before estimating the model, we begin by examining summary statistics and missing values in our item response data. To begin, we will show summary statistics of the fraction correct on the language and math sections of the examination, as well as the fraction correct on broad sub-domains.

The sub-domains for the language section are:

The sub-domains for the math section are:

## Joining, by = "name"
Table 1: Summary Statistics of Fraction Correct on Language Assessment Domains for Teachers
Item Label Mean Std Dev Min 25th Percentile Median 75th Percentile Max # Complete Cases # Missing Cases Histogram
cloze Cloze task 0.62 0.26 0 0.45 0.73 0.82 1 377 0 ▂▂▅▂▃▇▅▅
grammar Grammar task 0.81 0.23 0 0.67 0.83 1 1 377 0 ▁▁▁▂▁▃▅▇
literacy_content_knowledge Fraction correct language 0.7 0.2 0 0.6 0.75 0.85 1 377 0 ▁▁▁▃▅▇▆▆
read_passage Read the passage 0.79 0.31 0 0.67 1 1 1 377 0 ▁▁▁▁▁▃▁▇
Note:
Summary table shows unweighted summary statistics from teacher language assessment.
## Joining, by = "name"
Table 2: Summary Statistics of Fraction Correct on Math Assessment Domains for Teachers
Item Label Mean Std Dev Min 25th Percentile Median 75th Percentile Max # Complete Cases # Missing Cases Histogram
arithmetic_number_relations Arithmetic and number relations 0.64 0.25 0.071 0.43 0.64 0.86 1 384 0 ▂▃▂▅▇▃▇▅
geometry Geometry 0.66 0.31 0 0.5 0.75 1 1 384 0 ▁▅▁▅▁▅▁▇
interpret_data Interpret Data 0.67 0.29 0 0.4 0.8 0.8 1 384 0 ▂▃▁▅▆▁▇▆
math_content_knowledge Fraction correct math 0.65 0.24 0.043 0.48 0.7 0.87 1 384 0 ▁▃▅▅▃▇▇▅
Note:
Summary table shows unweighted summary statistics from teacher math assessment.

Item Level Summary Statistics

Next, we display summary statistics at the item level for our language and mathematics assessment.

Table 3: Summary Statistics of Language Assessment Items for Teachers
Item Label Mean Std Dev Min 25th Percentile Median 75th Percentile Max # Complete Cases # Missing Cases Histogram
m5s1q1a_grammer (Unless, If, Perhaps, Although) you tidy up your room, you won’t get candy. 0.57 0.5 0 0 1 1 1 377 0 ▆▁▁▁▁▁▁▇
m5s1q1b_grammer (When, If, Because, Although) I was telling the truth, my mother didn’t believe 0.8 0.4 0 1 1 1 1 377 0 ▂▁▁▁▁▁▁▇
m5s1q1c_grammer A person who (which, who, when, may) flies an airplane is a pilot. 0.85 0.36 0 1 1 1 1 377 0 ▂▁▁▁▁▁▁▇
m5s1q1d_grammer My sister likes to read, so (so, although, perhaps, when) I have boug 0.9 0.3 0 1 1 1 1 377 0 ▁▁▁▁▁▁▁▇
m5s1q1e_grammer If I were a doctor, I shall (will, would, shall, am able to) work i 0.79 0.41 0 1 1 1 1 377 0 ▂▁▁▁▁▁▁▇
m5s1q1f_grammer The accident had seen (see, saw, had seen, was seen) by three people 0.93 0.26 0 1 1 1 1 377 0 ▁▁▁▁▁▁▁▇
m5s1q2a_cloze Javid, it is (a) half past seven. 0.59 0.49 0 0 1 1 1 377 0 ▅▁▁▁▁▁▁▇
m5s1q2b_cloze Get (b) . 0.29 0.45 0 0 0 1 1 377 0 ▇▁▁▁▁▁▁▃
m5s1q2c_cloze Today there is a (c) big football match at school. 0.64 0.48 0 0 1 1 1 377 0 ▅▁▁▁▁▁▁▇
m5s1q2d_cloze Juma: Father, I (d) want not go to school. 0.66 0.47 0 0 1 1 1 377 0 ▅▁▁▁▁▁▁▇
m5s1q2e_cloze I am (e) scared to go. 0.89 0.32 0 1 1 1 1 377 0 ▁▁▁▁▁▁▁▇
m5s1q2f_cloze Everyone (f) hates me. 0.64 0.48 0 0 1 1 1 377 0 ▅▁▁▁▁▁▁▇
m5s1q2g_cloze The players want to beat (g) . 0.77 0.42 0 1 1 1 1 377 0 ▃▁▁▁▁▁▁▇
m5s1q2h_cloze
  1. Where do I have to go to school?
0.32 0.47 0 0 0 1 1 377 0 ▇▁▁▁▁▁▁▅
m5s1q2i_cloze Father: You are going and that is final. I will give you two (i) 0.62 0.49 0 0 1 1 1 377 0 ▆▁▁▁▁▁▁▇
m5s1q2j_cloze have to go to school today. First, you are 40 (j) years old. 0.71 0.45 0 0 1 1 1 377 0 ▅▁▁▁▁▁▁▇
m5s1q2k_cloze Javid, it is (a) half past seven. 0.71 0.45 0 0 1 1 1 377 0 ▅▁▁▁▁▁▁▇
m5s1q4a_passage 4a. Why did the animals huddle together beneath the bushes? 0.81 0.39 0 1 1 1 1 377 0 ▂▁▁▁▁▁▁▇
m5s1q4b_passage 4b. “His big eyes widened like saucers.” What do these words from the story tell 0.84 0.37 0 1 1 1 1 377 0 ▂▁▁▁▁▁▁▇
m5s1q4c_passage 4c. What made the roaring sound in the distance? 0.72 0.45 0 0 1 1 1 376 1 ▃▁▁▁▁▁▁▇
m5sb_tnum Please enter Teacher’s roster number 6.6 5.54 1 2 5 10 20 377 0 ▇▃▁▁▁▁▁▁
school_code NA 530182.84 323884.99 62181 283416 436493 662346 1731926 377 0 ▅▇▃▂▁▁▁▁
Note:
Summary table shows unweighted summary statistics from teacher language assessment.
Table 4: Summary Statistics of Math Assessment Items for Teachers
Item Label Mean Std Dev Min 25th Percentile Median 75th Percentile Max # Complete Cases # Missing Cases Histogram
m5s2q10a_data 10a. Look at the graph. How far has Joe ridden after 6 hours? 0.72 0.45 0 0 1 1 1 384 0 ▅▁▁▁▁▁▁▇
m5s2q10b_data 10b. Chan started riding at 8.30 in the morning. How far had he gone at 12.00pm? 0.34 0.47 0 0 0 1 1 384 0 ▇▁▁▁▁▁▁▃
m5s2q11a_number 11a. √(144= )12 0.87 0.33 0 1 1 1 1 384 0 ▂▁▁▁▁▁▁▇
m5s2q11b_number 11b. 12.15-11.83= 0.32 0.82 0.39 0 1 1 1 1 384 0 ▂▁▁▁▁▁▁▇
m5s2q11c_number 11c. 3/4÷7/8= 21/32 0.43 0.5 0 0 0 1 1 384 0 ▇▁▁▁▁▁▁▅
m5s2q12_number
  1. What is n?
0.45 0.5 0 0 0 1 1 384 0 ▇▁▁▁▁▁▁▆
m5s2q13a_geometric 13a. (a) Perimeter: 0.55 0.5 0 0 1 1 1 384 0 ▆▁▁▁▁▁▁▇
m5s2q13b_geometric 13b. (b) Area: 90 cm2 0.49 0.5 0 0 0 1 1 384 0 ▇▁▁▁▁▁▁▇
m5s2q1a_number 1a. 5/8 +1/4= 6/12 0.44 0.5 0 0 0 1 1 384 0 ▇▁▁▁▁▁▁▆
m5s2q1b_number 1b. √36- √9= √27 0.51 0.5 0 0 1 1 1 384 0 ▇▁▁▁▁▁▁▇
m5s2q1c_number 1c. 343+215+127= 685 0.9 0.3 0 1 1 1 1 384 0 ▁▁▁▁▁▁▁▇
m5s2q1d_number 1d. 72÷9= 7 0.69 0.46 0 0 1 1 1 384 0 ▃▁▁▁▁▁▁▇
m5s2q1e_number 1e. 37×13 = 3711 0.72 0.45 0 0 1 1 1 384 0 ▃▁▁▁▁▁▁▇
m5s2q2_number
  1. Which two numbers add up to make 0.81?
0.75 0.43 0 1 1 1 1 384 0 ▂▁▁▁▁▁▁▇
m5s2q3_number
  1. Circle the one that gives the smallest answer?
0.85 0.36 0 1 1 1 1 384 0 ▂▁▁▁▁▁▁▇
m5s2q4a_number 4a. Complete these fractions so that they are equivalent 0.49 0.5 0 0 0 1 1 384 0 ▇▁▁▁▁▁▁▆
m5s2q4b_number 4b. Complete these fractions so that they are equivalent 0.4 0.49 0 0 0 1 1 384 0 ▇▁▁▁▁▁▁▅
m5s2q5_number
  1. 2 exercise books cost 14 Kips. What is the cost of 15 exercise books?
0.7 0.46 0 0 1 1 1 384 0 ▃▁▁▁▁▁▁▇
m5s2q6_geometric
  1. How many sides does a triangle have?
0.94 0.24 0 1 1 1 1 384 0 ▁▁▁▁▁▁▁▇
m5s2q7_geometric
  1. Lines that cannot meet are lines
0.67 0.47 0 0 1 1 1 384 0 ▅▁▁▁▁▁▁▇
m5s2q8_data
  1. What time did Chanla arrive?
0.81 0.39 0 1 1 1 1 384 0 ▂▁▁▁▁▁▁▇
m5s2q9a_data 9a. How many people had cats? 0.7 0.46 0 0 1 1 1 384 0 ▅▁▁▁▁▁▁▇
m5s2q9b_data 9b. Which animal was the least popular? 0.78 0.42 0 1 1 1 1 384 0 ▃▁▁▁▁▁▁▇
m5sb_tnum Please enter Teacher’s roster number 6.84 6.75 1 3 5 9 83 384 0 ▇▁▁▁▁▁▁▁
school_code NA 534678.72 327628.34 62181 3e+05 436493 662346 1760396 384 0 ▃▇▃▂▁▁▁▁
Note:
Summary table shows unweighted summary statistics from teacher math assessment.

Inter-Item Correlations

Next we display inter-item correlations for our language and math teacher assessment.

Reliability and Confirmatory Factor Analysis

In Psychometrics, internal consistency is an estimate of test reliability. Cronbach’s Alpha (and other internal consistency coefficients) can take values between 0 and 1, being tests more consistent as the value of this coefficient approaches to 1.

In addition to the internal consistency coefficient for a construct, internal consistency analyses also include item level statistics of internal consistency and item discrimination. You will notice in the output of the alpha() function three additional data frames: Reliability if an item is dropped, Item statistics, and Non missing response frequency for each item. We are interested in the first two data frames.

In the case of the data frame “Reliability if an item is dropped”, we need to check what happens with the overall Cronbach’s alpha reliability when a given item is excluded from the analysis. This analysis allows us to identify inconsistent items when Cronbach’s Alpha increases once a given item is excluded. This information will be shown in the first column of that data frame.

In the case of the data frame “Item Statistics”, we want to identify the item correlation with the construct observed total score when the item is excluded from that total score. Ideally, we want items with a positive correlation between each item and the total score, otherwise that item is probably not measuring the same construct as the others, does not correctly discriminate among examinees, or has a problem in either its content or scoring procedure. From this data frame, we are interested in the fifth column titled “r.drop”.

Internal consistency for literacy items. Cronbach’s alpha = 0.80. Good reliability

For each of our language and math constructs (Language: cloze, grammar, read_passage; Math: arithmetic_number_relations, geometry, interpret_data), we report: Cronbach’s alpha for the whole test, Cronbach’s alpha increase or decrease when a given item is removed, and item-total construct score correlation (which is a CTT estimate of item discrimination).

Table 5: Internal Consistency for Cloze task items
Cronbach alpha for the whole test Cronbach alpha increase or decrease when a given item is removed Item-total construct score correlation
m5s1q2a_cloze 0.7953157 0.7711747 0.5240091
m5s1q2b_cloze 0.7953157 0.8015499 0.2291827
m5s1q2c_cloze 0.7953157 0.7631229 0.5951171
m5s1q2d_cloze 0.7953157 0.7561969 0.6572719
m5s1q2e_cloze 0.7953157 0.7976091 0.2292297
m5s1q2f_cloze 0.7953157 0.7639766 0.5883499
m5s1q2g_cloze 0.7953157 0.7984915 0.2601757
m5s1q2h_cloze 0.7953157 0.7900821 0.3517657
m5s1q2i_cloze 0.7953157 0.8066706 0.2051435
m5s1q2j_cloze 0.7953157 0.7512813 0.6971255
m5s1q2k_cloze 0.7953157 0.7581546 0.6383880
Table 6: Internal Consistency for Grammar task items
Cronbach alpha for the whole test Cronbach alpha increase or decrease when a given item is removed Item-total construct score correlation
m5s1q1a_grammer 0.6854414 0.6526996 0.4102313
m5s1q1b_grammer 0.6854414 0.6234375 0.4753926
m5s1q1c_grammer 0.6854414 0.7004999 0.2330251
m5s1q1d_grammer 0.6854414 0.6593655 0.3695725
m5s1q1e_grammer 0.6854414 0.6174713 0.4914113
m5s1q1f_grammer 0.6854414 0.6063424 0.5746573
Table 7: Internal Consistency for Read the Passage items
Cronbach alpha for the whole test Cronbach alpha increase or decrease when a given item is removed Item-total construct score correlation
m5s1q4a_passage 0.6902296 0.5629543 0.5338648
m5s1q4b_passage 0.6902296 0.5863464 0.5174464
m5s1q4c_passage 0.6902296 0.6489338 0.4749549
Table 8: Internal Consistency for Arithmetic & Number Relations items
Cronbach alpha for the whole test Cronbach alpha increase or decrease when a given item is removed Item-total construct score correlation
m5s2q1a_number 0.8297789 0.8070323 0.6186348
m5s2q1b_number 0.8297789 0.8177661 0.4801730
m5s2q1c_number 0.8297789 0.8314229 0.2262852
m5s2q1d_number 0.8297789 0.8121627 0.5590767
m5s2q1e_number 0.8297789 0.8126878 0.5524020
m5s2q2_number 0.8297789 0.8194443 0.4543922
m5s2q3_number 0.8297789 0.8250594 0.3616452
m5s2q4a_number 0.8297789 0.8311211 0.3004381
m5s2q4b_number 0.8297789 0.8131696 0.5404635
m5s2q5_number 0.8297789 0.8276083 0.3385494
m5s2q11a_number 0.8297789 0.8221927 0.4159423
m5s2q11b_number 0.8297789 0.8178824 0.4797554
m5s2q11c_number 0.8297789 0.8143780 0.5245147
m5s2q12_number 0.8297789 0.8109346 0.5685776
Table 9: Internal Consistency for Geometry items
Cronbach alpha for the whole test Cronbach alpha increase or decrease when a given item is removed Item-total construct score correlation
m5s2q6_geometric 0.6311091 0.7064357 0.0918728
m5s2q7_geometric 0.6311091 0.5880060 0.3807792
m5s2q13a_geometric 0.6311091 0.3962097 0.6023500
m5s2q13b_geometric 0.6311091 0.4185041 0.5777277
Table 10: Internal Consistency for Interpret Data items
Cronbach alpha for the whole test Cronbach alpha increase or decrease when a given item is removed Item-total construct score correlation
m5s2q8_data 0.6532352 0.6478732 0.2924829
m5s2q9a_data 0.6532352 0.5880597 0.4324043
m5s2q9b_data 0.6532352 0.5623142 0.4889833
m5s2q10a_data 0.6532352 0.5731189 0.4612784
m5s2q10b_data 0.6532352 0.6236595 0.3589469

IRT Parameters

The tables below show the IRT parameter estimates from our 2PL model.

#create matrix with  just item responses
math <- teacher_assessment_math %>%
  select(-c(school_code, m5sb_tnum))

language <- teacher_assessment_language %>%
  select(-c(school_code, m5sb_tnum))

#Estimate IRT parameters ignoring missing values
irt_math_2PL <- mirt(math, 1, itemtype='2PL', optimizer='NR', SE=FALSE, technical=list(removeEmptyRows=TRUE))
## 
Iteration: 1, Log-Lik: -4355.076, Max-Change: 0.77616
Iteration: 2, Log-Lik: -4228.942, Max-Change: 0.37144
Iteration: 3, Log-Lik: -4206.642, Max-Change: 0.21762
Iteration: 4, Log-Lik: -4198.099, Max-Change: 0.14399
Iteration: 5, Log-Lik: -4194.128, Max-Change: 0.10103
Iteration: 6, Log-Lik: -4192.154, Max-Change: 0.07305
Iteration: 7, Log-Lik: -4190.146, Max-Change: 0.02099
Iteration: 8, Log-Lik: -4190.057, Max-Change: 0.01610
Iteration: 9, Log-Lik: -4190.007, Max-Change: 0.01214
Iteration: 10, Log-Lik: -4189.943, Max-Change: 0.00302
Iteration: 11, Log-Lik: -4189.940, Max-Change: 0.00223
Iteration: 12, Log-Lik: -4189.938, Max-Change: 0.00167
Iteration: 13, Log-Lik: -4189.932, Max-Change: 0.00102
Iteration: 14, Log-Lik: -4189.932, Max-Change: 0.00091
Iteration: 15, Log-Lik: -4189.932, Max-Change: 0.00082
Iteration: 16, Log-Lik: -4189.930, Max-Change: 0.00033
Iteration: 17, Log-Lik: -4189.930, Max-Change: 0.00030
Iteration: 18, Log-Lik: -4189.930, Max-Change: 0.00027
Iteration: 19, Log-Lik: -4189.930, Max-Change: 0.00011
Iteration: 20, Log-Lik: -4189.930, Max-Change: 0.00010
coef(irt_math_2PL, IRTpars=TRUE, as.data.frame=TRUE) %>%
  kable() %>%
  kable_styling()
par
m5s2q1a_number.a 2.4442524
m5s2q1a_number.b 0.2712299
m5s2q1a_number.g 0.0000000
m5s2q1a_number.u 1.0000000
m5s2q1b_number.a 1.3658375
m5s2q1b_number.b 0.1460926
m5s2q1b_number.g 0.0000000
m5s2q1b_number.u 1.0000000
m5s2q1c_number.a 0.7752071
m5s2q1c_number.b -2.9958323
m5s2q1c_number.g 0.0000000
m5s2q1c_number.u 1.0000000
m5s2q1d_number.a 1.9000747
m5s2q1d_number.b -0.7742794
m5s2q1d_number.g 0.0000000
m5s2q1d_number.u 1.0000000
m5s2q1e_number.a 1.9523169
m5s2q1e_number.b -0.7972886
m5s2q1e_number.g 0.0000000
m5s2q1e_number.u 1.0000000
m5s2q2_number.a 1.3209676
m5s2q2_number.b -1.1357770
m5s2q2_number.g 0.0000000
m5s2q2_number.u 1.0000000
m5s2q3_number.a 1.1557034
m5s2q3_number.b -1.6895256
m5s2q3_number.g 0.0000000
m5s2q3_number.u 1.0000000
m5s2q4a_number.a 0.7175522
m5s2q4a_number.b 0.3781112
m5s2q4a_number.g 0.0000000
m5s2q4a_number.u 1.0000000
m5s2q4b_number.a 2.1269563
m5s2q4b_number.b 0.4352167
m5s2q4b_number.g 0.0000000
m5s2q4b_number.u 1.0000000
m5s2q5_number.a 0.9669884
m5s2q5_number.b -0.9234079
m5s2q5_number.g 0.0000000
m5s2q5_number.u 1.0000000
m5s2q6_geometric.a 0.7703682
m5s2q6_geometric.b -4.3371005
m5s2q6_geometric.g 0.0000000
m5s2q6_geometric.u 1.0000000
m5s2q7_geometric.a 1.2579029
m5s2q7_geometric.b -0.5923030
m5s2q7_geometric.g 0.0000000
m5s2q7_geometric.u 1.0000000
m5s2q8_data.a 0.9376925
m5s2q8_data.b -1.8271261
m5s2q8_data.g 0.0000000
m5s2q8_data.u 1.0000000
m5s2q9a_data.a 1.2982132
m5s2q9a_data.b -0.6858850
m5s2q9a_data.g 0.0000000
m5s2q9a_data.u 1.0000000
m5s2q9b_data.a 1.5972827
m5s2q9b_data.b -0.9602406
m5s2q9b_data.g 0.0000000
m5s2q9b_data.u 1.0000000
m5s2q10a_data.a 1.6915963
m5s2q10a_data.b -0.4793811
m5s2q10a_data.g 0.0000000
m5s2q10a_data.u 1.0000000
m5s2q10b_data.a 1.6026208
m5s2q10b_data.b 0.7214238
m5s2q10b_data.g 0.0000000
m5s2q10b_data.u 1.0000000
m5s2q11a_number.a 1.9791521
m5s2q11a_number.b -1.4334109
m5s2q11a_number.g 0.0000000
m5s2q11a_number.u 1.0000000
m5s2q11b_number.a 1.7488348
m5s2q11b_number.b -1.0768108
m5s2q11b_number.g 0.0000000
m5s2q11b_number.u 1.0000000
m5s2q11c_number.a 1.9915238
m5s2q11c_number.b 0.4719436
m5s2q11c_number.g 0.0000000
m5s2q11c_number.u 1.0000000
m5s2q12_number.a 2.2128578
m5s2q12_number.b 0.2444848
m5s2q12_number.g 0.0000000
m5s2q12_number.u 1.0000000
m5s2q13a_geometric.a 2.7449964
m5s2q13a_geometric.b -0.2255125
m5s2q13a_geometric.g 0.0000000
m5s2q13a_geometric.u 1.0000000
m5s2q13b_geometric.a 2.2583454
m5s2q13b_geometric.b -0.0112839
m5s2q13b_geometric.g 0.0000000
m5s2q13b_geometric.u 1.0000000
GroupPars.MEAN_1 0.0000000
GroupPars.COV_11 1.0000000
irt_lang_2PL <- mirt(language, 1, itemtype='2PL',optimizer='NR',  SE=FALSE, technical=list(removeEmptyRows=TRUE))
## 
Iteration: 1, Log-Lik: -3811.491, Max-Change: 0.70531
Iteration: 2, Log-Lik: -3749.645, Max-Change: 0.63370
Iteration: 3, Log-Lik: -3720.109, Max-Change: 0.62401
Iteration: 4, Log-Lik: -3702.372, Max-Change: 0.57622
Iteration: 5, Log-Lik: -3692.954, Max-Change: 0.48877
Iteration: 6, Log-Lik: -3688.568, Max-Change: 0.39341
Iteration: 7, Log-Lik: -3685.132, Max-Change: 0.14437
Iteration: 8, Log-Lik: -3684.965, Max-Change: 0.11910
Iteration: 9, Log-Lik: -3684.865, Max-Change: 0.09931
Iteration: 10, Log-Lik: -3684.666, Max-Change: 0.02787
Iteration: 11, Log-Lik: -3684.653, Max-Change: 0.02056
Iteration: 12, Log-Lik: -3684.645, Max-Change: 0.01600
Iteration: 13, Log-Lik: -3684.627, Max-Change: 0.00492
Iteration: 14, Log-Lik: -3684.624, Max-Change: 0.00464
Iteration: 15, Log-Lik: -3684.622, Max-Change: 0.00416
Iteration: 16, Log-Lik: -3684.615, Max-Change: 0.00162
Iteration: 17, Log-Lik: -3684.615, Max-Change: 0.00148
Iteration: 18, Log-Lik: -3684.615, Max-Change: 0.00136
Iteration: 19, Log-Lik: -3684.614, Max-Change: 0.00070
Iteration: 20, Log-Lik: -3684.614, Max-Change: 0.00061
Iteration: 21, Log-Lik: -3684.614, Max-Change: 0.00054
Iteration: 22, Log-Lik: -3684.614, Max-Change: 0.00025
Iteration: 23, Log-Lik: -3684.614, Max-Change: 0.00024
Iteration: 24, Log-Lik: -3684.614, Max-Change: 0.00022
Iteration: 25, Log-Lik: -3684.614, Max-Change: 0.00012
Iteration: 26, Log-Lik: -3684.614, Max-Change: 0.00010
Iteration: 27, Log-Lik: -3684.614, Max-Change: 0.00009
coef(irt_lang_2PL, IRTpars=TRUE, as.data.frame=TRUE) %>%
  kable() %>%
  kable_styling()
par
m5s1q1a_grammer.a 0.8175140
m5s1q1a_grammer.b -0.4677988
m5s1q1a_grammer.g 0.0000000
m5s1q1a_grammer.u 1.0000000
m5s1q1b_grammer.a 0.7618566
m5s1q1b_grammer.b -1.8055815
m5s1q1b_grammer.g 0.0000000
m5s1q1b_grammer.u 1.0000000
m5s1q1c_grammer.a 0.5917136
m5s1q1c_grammer.b -2.7363199
m5s1q1c_grammer.g 0.0000000
m5s1q1c_grammer.u 1.0000000
m5s1q1d_grammer.a 1.0994252
m5s1q1d_grammer.b -2.0339173
m5s1q1d_grammer.g 0.0000000
m5s1q1d_grammer.u 1.0000000
m5s1q1e_grammer.a 0.7478449
m5s1q1e_grammer.b -1.7889671
m5s1q1e_grammer.g 0.0000000
m5s1q1e_grammer.u 1.0000000
m5s1q1f_grammer.a 1.1217430
m5s1q1f_grammer.b -2.2350878
m5s1q1f_grammer.g 0.0000000
m5s1q1f_grammer.u 1.0000000
m5s1q2a_cloze.a 1.9152780
m5s1q2a_cloze.b -0.3935916
m5s1q2a_cloze.g 0.0000000
m5s1q2a_cloze.u 1.0000000
m5s1q2b_cloze.a 0.6198855
m5s1q2b_cloze.b 1.6619209
m5s1q2b_cloze.g 0.0000000
m5s1q2b_cloze.u 1.0000000
m5s1q2c_cloze.a 2.3269704
m5s1q2c_cloze.b -0.4367561
m5s1q2c_cloze.g 0.0000000
m5s1q2c_cloze.u 1.0000000
m5s1q2d_cloze.a 3.3052049
m5s1q2d_cloze.b -0.4486762
m5s1q2d_cloze.g 0.0000000
m5s1q2d_cloze.u 1.0000000
m5s1q2e_cloze.a 0.6677942
m5s1q2e_cloze.b -3.3581175
m5s1q2e_cloze.g 0.0000000
m5s1q2e_cloze.u 1.0000000
m5s1q2f_cloze.a 2.7182230
m5s1q2f_cloze.b -0.4360568
m5s1q2f_cloze.g 0.0000000
m5s1q2f_cloze.u 1.0000000
m5s1q2g_cloze.a 0.6450082
m5s1q2g_cloze.b -1.6262678
m5s1q2g_cloze.g 0.0000000
m5s1q2g_cloze.u 1.0000000
m5s1q2h_cloze.a 1.0258080
m5s1q2h_cloze.b 0.7698623
m5s1q2h_cloze.g 0.0000000
m5s1q2h_cloze.u 1.0000000
m5s1q2i_cloze.a 0.6118441
m5s1q2i_cloze.b -0.3279676
m5s1q2i_cloze.g 0.0000000
m5s1q2i_cloze.u 1.0000000
m5s1q2j_cloze.a 5.8873397
m5s1q2j_cloze.b -0.3622293
m5s1q2j_cloze.g 0.0000000
m5s1q2j_cloze.u 1.0000000
m5s1q2k_cloze.a 4.0690330
m5s1q2k_cloze.b -0.3807108
m5s1q2k_cloze.g 0.0000000
m5s1q2k_cloze.u 1.0000000
m5s1q4a_passage.a 0.7613037
m5s1q4a_passage.b -2.1332402
m5s1q4a_passage.g 0.0000000
m5s1q4a_passage.u 1.0000000
m5s1q4b_passage.a 1.0349799
m5s1q4b_passage.b -1.8045033
m5s1q4b_passage.g 0.0000000
m5s1q4b_passage.u 1.0000000
m5s1q4c_passage.a 0.6568010
m5s1q4c_passage.b -1.5335950
m5s1q4c_passage.g 0.0000000
m5s1q4c_passage.u 1.0000000
GroupPars.MEAN_1 0.0000000
GroupPars.COV_11 1.0000000
#estimate factor scores from models
lang_teach_scores<-data.frame(fscores(irt_lang_2PL, method='EAP', response.pattern = language))

math_teach_scores<-data.frame(fscores(irt_math_2PL, method='EAP', response.pattern = math))

#merge scores back onto

Plots of Test Information Function and Test Reliability Function

Below we plot the test information and test reliability functions estimated from our 2PL IRT model.

Item Information Functions

Below is a plot of the item information functions for all of our math and language items. Specific items can be displayed by using the filters in the sidebars.

SDI Comparison

Next, we examine how teachers in Peru compare to teachers in other countries that have taken a similar examination. The Service Delivery Indicator survey has been deployed in several countries, mostly in Sub-Saharan Africa. The teacher assessment used is very similar to the one used in the Peru Dashboard survey. In fact, the Peru test instrument was taken directly from the SDI instrument, with a few modifications. A ‘read the passage’ item was added to our instrument, which differs from most SDI assessments. Additionally, two arithmetic and number relations math problems on square roots and adding fractions were added to make our math assessment more difficult.

The list of overlapping items is below.

## [1] "The following items in Language overlapped in SDI and the Dashboard:"
##  [1] "m5s1q1a_grammer" "m5s1q1b_grammer" "m5s1q1c_grammer"
##  [4] "m5s1q1d_grammer" "m5s1q1e_grammer" "m5s1q1f_grammer"
##  [7] "m5s1q2a_cloze"   "m5s1q2b_cloze"   "m5s1q2c_cloze"  
## [10] "m5s1q2d_cloze"   "m5s1q2e_cloze"   "m5s1q2f_cloze"  
## [13] "m5s1q2g_cloze"   "m5s1q2h_cloze"   "m5s1q2i_cloze"  
## [16] "m5s1q2j_cloze"   "m5s1q2k_cloze"
## [1] "The following items in Math overlapped in SDI and the Dashboard:"
##  [1] "m5s2q1c_number"     "m5s2q1d_number"     "m5s2q1e_number"    
##  [4] "m5s2q2_number"      "m5s2q3_number"      "m5s2q4a_number"    
##  [7] "m5s2q4b_number"     "m5s2q5_number"      "m5s2q6_geometric"  
## [10] "m5s2q7_geometric"   "m5s2q8_data"        "m5s2q9a_data"      
## [13] "m5s2q9b_data"       "m5s2q10a_data"      "m5s2q10b_data"     
## [16] "m5s2q11a_number"    "m5s2q11b_number"    "m5s2q11c_number"   
## [19] "m5s2q12_number"     "m5s2q13a_geometric" "m5s2q13b_geometric"

In what follows below, we will compare teacher latent ability scores for Peru using our Dashboard Survey to ability scores from the SDI survey in Kenya, Lao PDR, Madagascar, Morocco, Mozambique, and Tanzania.

Methodology for item equating

In order to equate the ability scores produced using the different instruments, we use an IRT equating method based on the common set of items. We use the ‘equateIRT’ R package to do so. https://cran.r-project.org/web/packages/equateIRT/equateIRT.pdf.

The goal of test equating in our case is to place scores from Dashboard survey and the SDI survey on a common scale, so that we can directly compare teacher latent ability across countries. We use the common set of items, listed above, to do the equating. A direct equating approach is used based on the Stocking-Lord approach.

Summary Statistics of Ability Scores

Below we show the distributions of teacher ability scores based on the IRT model estimates.

## Picking joint bandwidth of 0.0452
Table 11: Summary Statistics of Math Assessment Scores for Teachers Across Countries
countryname math_content_knowledge_mean math_content_knowledge_sd
Kenya 0.7559985 0.2114395
Lao PDR 0.4543115 0.2134898
Madagascar 0.2312355 0.1375563
Morocco 0.7311888 0.2361793
Mozambique 0.1227382 0.2098122
Peru 0.6696810 0.2376182
Tanzania 0.2675159 0.3272945
## Picking joint bandwidth of 0.0423
Table 12: Summary Statistics of Language Assessment Scores for Teachers Across Countries
countryname literacy_content_knowledge_mean literacy_content_knowledge_sd
Kenya 0.7613109 0.1632670
Lao PDR 0.7203196 0.2271848
Madagascar 0.3798607 0.2551291
Morocco 0.8379144 0.1900895
Mozambique 0.4641791 0.1922594
Peru 0.6867700 0.2140706
Tanzania 0.6851075 0.1906235

Summary Statistics SDI - Kenya

Table 13: Summary Statistics of Kenya Language Assessment Items for Teachers
Item Label Mean Std Dev Min 25th Percentile Median 75th Percentile Max # Complete Cases # Missing Cases Histogram
m5s1q1a_grammer (Unless, If, Perhaps, Although) you tidy up your room, you won’t get candy. 0.69 0.46 0 0 1 1 1 1679 0 ▃▁▁▁▁▁▁▇
m5s1q1b_grammer (When, If, Because, Although) I was telling the truth, my mother didn’t believe 0.92 0.27 0 1 1 1 1 1679 0 ▁▁▁▁▁▁▁▇
m5s1q1c_grammer A person who (which, who, when, may) flies an airplane is a pilot. 0.98 0.14 0 1 1 1 1 1679 0 ▁▁▁▁▁▁▁▇
m5s1q1d_grammer My sister likes to read, so (so, although, perhaps, when) I have boug 0.92 0.27 0 1 1 1 1 1679 0 ▁▁▁▁▁▁▁▇
m5s1q1e_grammer If I were a doctor, I shall (will, would, shall, am able to) work i 0.93 0.26 0 1 1 1 1 1679 0 ▁▁▁▁▁▁▁▇
m5s1q1f_grammer The accident had seen (see, saw, had seen, was seen) by three people 0.94 0.23 0 1 1 1 1 1679 0 ▁▁▁▁▁▁▁▇
m5s1q2a_cloze Javid, it is (a) half past seven. 0.84 0.37 0 1 1 1 1 1679 0 ▂▁▁▁▁▁▁▇
m5s1q2b_cloze Get (b) . 0.86 0.34 0 1 1 1 1 1679 0 ▁▁▁▁▁▁▁▇
m5s1q2c_cloze Today there is a (c) big football match at school. 0.62 0.48 0 0 1 1 1 1679 0 ▅▁▁▁▁▁▁▇
m5s1q2d_cloze Juma: Father, I (d) want not go to school. 0.4 0.49 0 0 0 1 1 1679 0 ▇▁▁▁▁▁▁▅
m5s1q2e_cloze I am (e) scared to go. 0.23 0.42 0 0 0 0 1 1679 0 ▇▁▁▁▁▁▁▂
m5s1q2f_cloze Everyone (f) hates me. 0.82 0.39 0 1 1 1 1 1679 0 ▂▁▁▁▁▁▁▇
m5s1q2g_cloze The players want to beat (g) . 0.76 0.43 0 1 1 1 1 1679 0 ▃▁▁▁▁▁▁▇
m5s1q2h_cloze
  1. Where do I have to go to school?
0.69 0.46 0 0 1 1 1 1679 0 ▅▁▁▁▁▁▁▇
m5s1q2i_cloze Father: You are going and that is final. I will give you two (i) 0.88 0.33 0 1 1 1 1 1679 0 ▂▁▁▁▁▁▁▇
m5s1q2j_cloze have to go to school today. First, you are 40 (j) years old. 0.79 0.4 0 1 1 1 1 1679 0 ▂▁▁▁▁▁▁▇
m5s1q2k_cloze Javid, it is (a) half past seven. 0.68 0.47 0 0 1 1 1 1679 0 ▃▁▁▁▁▁▁▇
m6sa1q1a NA 0.98 0.12 0 1 1 1 1 1679 0 ▁▁▁▁▁▁▁▇
m6sa1q1b NA 0.97 0.18 0 1 1 1 1 1679 0 ▁▁▁▁▁▁▁▇
m6sa1q1c NA 0.97 0.18 0 1 1 1 1 1679 0 ▁▁▁▁▁▁▁▇
m6sa1q1d NA 0.93 0.25 0 1 1 1 1 1679 0 ▁▁▁▁▁▁▁▇
Note:
Summary table shows unweighted summary statistics from teacher language assessment.
Table 14: Summary Statistics of Kenya Math Assessment Items for Teachers
Item Label Mean Std Dev Min 25th Percentile Median 75th Percentile Max # Complete Cases # Missing Cases Histogram
m5s2q10a_data 10a. Look at the graph. How far has Joe ridden after 6 hours? 0.8 0.4 0 1 1 1 1 1679 0 ▂▁▁▁▁▁▁▇
m5s2q10b_data 10b. Chan started riding at 8.30 in the morning. How far had he gone at 12.00pm? 0.45 0.5 0 0 0 1 1 1679 0 ▇▁▁▁▁▁▁▆
m5s2q11a_number 11a. √(144= )12 0.87 0.34 0 1 1 1 1 1679 0 ▁▁▁▁▁▁▁▇
m5s2q11b_number 11b. 12.15-11.83= 0.32 0.81 0.39 0 1 1 1 1 1679 0 ▂▁▁▁▁▁▁▇
m5s2q11c_number 11c. 3/4÷7/8= 21/32 0.67 0.47 0 0 1 1 1 1679 0 ▃▁▁▁▁▁▁▇
m5s2q12_number
  1. What is n?
0.71 0.45 0 0 1 1 1 1679 0 ▃▁▁▁▁▁▁▇
m5s2q13a_geometric 13a. (a) Perimeter: 0.79 0.41 0 1 1 1 1 1679 0 ▂▁▁▁▁▁▁▇
m5s2q13b_geometric 13b. (b) Area: 90 cm2 0.73 0.44 0 0 1 1 1 1679 0 ▃▁▁▁▁▁▁▇
m5s2q1c_number 1c. 343+215+127= 685 0.88 0.33 0 1 1 1 1 1679 0 ▁▁▁▁▁▁▁▇
m5s2q1d_number 1d. 72÷9= 7 0.87 0.34 0 1 1 1 1 1679 0 ▁▁▁▁▁▁▁▇
m5s2q1e_number 1e. 37×13 = 3711 0.87 0.33 0 1 1 1 1 1679 0 ▁▁▁▁▁▁▁▇
m5s2q2_number
  1. Which two numbers add up to make 0.81?
0.77 0.42 0 1 1 1 1 1679 0 ▂▁▁▁▁▁▁▇
m5s2q3_number
  1. Circle the one that gives the smallest answer?
0.9 0.3 0 1 1 1 1 1679 0 ▁▁▁▁▁▁▁▇
m5s2q4a_number 4a. Complete these fractions so that they are equivalent 0.4 0.49 0 0 0 1 1 1679 0 ▇▁▁▁▁▁▁▆
m5s2q4b_number 4b. Complete these fractions so that they are equivalent 0.47 0.5 0 0 0 1 1 1679 0 ▇▁▁▁▁▁▁▇
m5s2q5_number
  1. 2 exercise books cost 14 Kips. What is the cost of 15 exercise books?
0.83 0.38 0 1 1 1 1 1679 0 ▂▁▁▁▁▁▁▇
m5s2q6_geometric
  1. How many sides does a triangle have?
0.94 0.24 0 1 1 1 1 1679 0 ▁▁▁▁▁▁▁▇
m5s2q7_geometric
  1. Lines that cannot meet are lines
0.93 0.25 0 1 1 1 1 1679 0 ▁▁▁▁▁▁▁▇
m5s2q8_data
  1. What time did Chanla arrive?
0.78 0.41 0 1 1 1 1 1679 0 ▂▁▁▁▁▁▁▇
m5s2q9a_data 9a. How many people had cats? 0.63 0.48 0 0 1 1 1 1679 0 ▅▁▁▁▁▁▁▇
m5s2q9b_data 9b. Which animal was the least popular? 0.77 0.42 0 1 1 1 1 1679 0 ▂▁▁▁▁▁▁▇
m6sa2q1a NA 0.97 0.17 0 1 1 1 1 1679 0 ▁▁▁▁▁▁▁▇
m6sa2q1b NA 0.88 0.33 0 1 1 1 1 1679 0 ▁▁▁▁▁▁▁▇
Note:
Summary table shows unweighted summary statistics from teacher math assessment.

Summary Statistics SDI - Mozambique

Table 15: Summary Statistics of Mozambique Language Assessment Items for Teachers
Item Label Mean Std Dev Min 25th Percentile Median 75th Percentile Max # Complete Cases # Missing Cases Histogram
m5s1q1a_grammer (Unless, If, Perhaps, Although) you tidy up your room, you won’t get candy. 0.13 0.34 0 0 0 0 1 1343 0 ▇▁▁▁▁▁▁▁
m5s1q1b_grammer (When, If, Because, Although) I was telling the truth, my mother didn’t believe 0.33 0.47 0 0 0 1 1 1343 0 ▇▁▁▁▁▁▁▃
m5s1q1c_grammer A person who (which, who, when, may) flies an airplane is a pilot. 0.43 0.5 0 0 0 1 1 1343 0 ▇▁▁▁▁▁▁▆
m5s1q1d_grammer My sister likes to read, so (so, although, perhaps, when) I have boug 0.45 0.5 0 0 0 1 1 1343 0 ▇▁▁▁▁▁▁▆
m5s1q1e_grammer If I were a doctor, I shall (will, would, shall, am able to) work i 0.45 0.5 0 0 0 1 1 1343 0 ▇▁▁▁▁▁▁▆
m5s1q1f_grammer The accident had seen (see, saw, had seen, was seen) by three people 0.45 0.5 0 0 0 1 1 1343 0 ▇▁▁▁▁▁▁▆
m5s1q2a_cloze Javid, it is (a) half past seven. 0.24 0.43 0 0 0 0 1 1343 0 ▇▁▁▁▁▁▁▂
m5s1q2b_cloze Get (b) . 0.14 0.35 0 0 0 0 1 1343 0 ▇▁▁▁▁▁▁▁
m5s1q2c_cloze Today there is a (c) big football match at school. 0.28 0.45 0 0 0 1 1 1343 0 ▇▁▁▁▁▁▁▃
m5s1q2d_cloze Juma: Father, I (d) want not go to school. 0.25 0.43 0 0 0 0 1 1343 0 ▇▁▁▁▁▁▁▂
m5s1q2e_cloze I am (e) scared to go. 0.12 0.32 0 0 0 0 1 1343 0 ▇▁▁▁▁▁▁▁
m5s1q2f_cloze Everyone (f) hates me. 0.15 0.36 0 0 0 0 1 1343 0 ▇▁▁▁▁▁▁▂
m5s1q2g_cloze The players want to beat (g) . 0.15 0.36 0 0 0 0 1 1343 0 ▇▁▁▁▁▁▁▂
m5s1q2h_cloze
  1. Where do I have to go to school?
0.041 0.2 0 0 0 0 1 1343 0 ▇▁▁▁▁▁▁▁
m5s1q2i_cloze Father: You are going and that is final. I will give you two (i) 0.02 0.14 0 0 0 0 1 1343 0 ▇▁▁▁▁▁▁▁
m5s1q2j_cloze have to go to school today. First, you are 40 (j) years old. 0.15 0.35 0 0 0 0 1 1343 0 ▇▁▁▁▁▁▁▂
m5s1q2k_cloze Javid, it is (a) half past seven. 0.17 0.38 0 0 0 0 1 1343 0 ▇▁▁▁▁▁▁▂
m6sa1q1a NA 0.47 0.5 0 0 0 1 1 1343 0 ▇▁▁▁▁▁▁▇
m6sa1q1b NA 0.46 0.5 0 0 0 1 1 1343 0 ▇▁▁▁▁▁▁▇
m6sa1q1c NA 0.44 0.5 0 0 0 1 1 1343 0 ▇▁▁▁▁▁▁▆
m6sa1q1d NA 0.45 0.5 0 0 0 1 1 1343 0 ▇▁▁▁▁▁▁▆
Note:
Summary table shows unweighted summary statistics from teacher language assessment.
Table 16: Summary Statistics of Mozambique Math Assessment Items for Teachers
Item Label Mean Std Dev Min 25th Percentile Median 75th Percentile Max # Complete Cases # Missing Cases Histogram
m5s2q10a_data 10a. Look at the graph. How far has Joe ridden after 6 hours? 0.11 0.32 0 0 0 0 1 1343 0 ▇▁▁▁▁▁▁▁
m5s2q10b_data 10b. Chan started riding at 8.30 in the morning. How far had he gone at 12.00pm? 0.021 0.14 0 0 0 0 1 1343 0 ▇▁▁▁▁▁▁▁
m5s2q11a_number 11a. √(144= )12 0.12 0.32 0 0 0 0 1 1343 0 ▇▁▁▁▁▁▁▁
m5s2q11b_number 11b. 12.15-11.83= 0.32 0.12 0.33 0 0 0 0 1 1343 0 ▇▁▁▁▁▁▁▁
m5s2q11c_number 11c. 3/4÷7/8= 21/32 0.05 0.22 0 0 0 0 1 1343 0 ▇▁▁▁▁▁▁▁
m5s2q12_number
  1. What is n?
0.038 0.19 0 0 0 0 1 1343 0 ▇▁▁▁▁▁▁▁
m5s2q13a_geometric 13a. (a) Perimeter: 0.062 0.24 0 0 0 0 1 1343 0 ▇▁▁▁▁▁▁▁
m5s2q13b_geometric 13b. (b) Area: 90 cm2 0.049 0.22 0 0 0 0 1 1343 0 ▇▁▁▁▁▁▁▁
m5s2q1c_number 1c. 343+215+127= 685 0.33 0.47 0 0 0 1 1 1343 0 ▇▁▁▁▁▁▁▃
m5s2q1d_number 1d. 72÷9= 7 0.27 0.44 0 0 0 1 1 1343 0 ▇▁▁▁▁▁▁▃
m5s2q1e_number 1e. 37×13 = 3711 0.27 0.44 0 0 0 1 1 1343 0 ▇▁▁▁▁▁▁▃
m5s2q2_number
  1. Which two numbers add up to make 0.81?
0.19 0.39 0 0 0 0 1 1343 0 ▇▁▁▁▁▁▁▂
m5s2q3_number
  1. Circle the one that gives the smallest answer?
0.22 0.41 0 0 0 0 1 1343 0 ▇▁▁▁▁▁▁▂
m5s2q4a_number 4a. Complete these fractions so that they are equivalent 0.051 0.22 0 0 0 0 1 1343 0 ▇▁▁▁▁▁▁▁
m5s2q4b_number 4b. Complete these fractions so that they are equivalent 0.044 0.21 0 0 0 0 1 1343 0 ▇▁▁▁▁▁▁▁
m5s2q5_number
  1. 2 exercise books cost 14 Kips. What is the cost of 15 exercise books?
0.13 0.33 0 0 0 0 1 1343 0 ▇▁▁▁▁▁▁▁
m5s2q6_geometric
  1. How many sides does a triangle have?
0.25 0.43 0 0 0 1 1 1343 0 ▇▁▁▁▁▁▁▃
m5s2q7_geometric
  1. Lines that cannot meet are lines
0.23 0.42 0 0 0 0 1 1343 0 ▇▁▁▁▁▁▁▂
m5s2q8_data
  1. What time did Chanla arrive?
0.11 0.31 0 0 0 0 1 1343 0 ▇▁▁▁▁▁▁▁
m5s2q9a_data 9a. How many people had cats? 0.1 0.31 0 0 0 0 1 1343 0 ▇▁▁▁▁▁▁▁
m5s2q9b_data 9b. Which animal was the least popular? 0.14 0.35 0 0 0 0 1 1343 0 ▇▁▁▁▁▁▁▁
m6sa2q1a NA 0.38 0.49 0 0 0 1 1 1343 0 ▇▁▁▁▁▁▁▅
m6sa2q1b NA 0.33 0.47 0 0 0 1 1 1343 0 ▇▁▁▁▁▁▁▃
Note:
Summary table shows unweighted summary statistics from teacher math assessment.

Summary Statistics SDI - LAO_PDR

Table 17: Summary Statistics of Lao PDR Language Assessment Items for Teachers
Item Label Mean Std Dev Min 25th Percentile Median 75th Percentile Max # Complete Cases # Missing Cases Histogram
m5s1q1a_grammer (Unless, If, Perhaps, Although) you tidy up your room, you won’t get candy. 0.44 0.5 0 0 0 1 1 740 0 ▇▁▁▁▁▁▁▆
m5s1q1b_grammer (When, If, Because, Although) I was telling the truth, my mother didn’t believe 0.41 0.49 0 0 0 1 1 740 0 ▇▁▁▁▁▁▁▆
m5s1q1c_grammer A person who (which, who, when, may) flies an airplane is a pilot. 0.84 0.37 0 1 1 1 1 740 0 ▂▁▁▁▁▁▁▇
m5s1q1d_grammer My sister likes to read, so (so, although, perhaps, when) I have boug 0.8 0.4 0 1 1 1 1 740 0 ▂▁▁▁▁▁▁▇
m5s1q1e_grammer If I were a doctor, I shall (will, would, shall, am able to) work i 0.85 0.36 0 1 1 1 1 740 0 ▂▁▁▁▁▁▁▇
m5s1q1f_grammer The accident had seen (see, saw, had seen, was seen) by three people 0.78 0.41 0 1 1 1 1 740 0 ▂▁▁▁▁▁▁▇
m5s1q2a_cloze Javid, it is (a) half past seven. 0 0 0 0 0 0 0 740 0 ▁▁▁▇▁▁▁▁
m5s1q2b_cloze Get (b) . 0 0 0 0 0 0 0 740 0 ▁▁▁▇▁▁▁▁
m5s1q2c_cloze Today there is a (c) big football match at school. 0 0 0 0 0 0 0 740 0 ▁▁▁▇▁▁▁▁
m5s1q2d_cloze Juma: Father, I (d) want not go to school. 0 0 0 0 0 0 0 740 0 ▁▁▁▇▁▁▁▁
m5s1q2e_cloze I am (e) scared to go. 0 0 0 0 0 0 0 740 0 ▁▁▁▇▁▁▁▁
m5s1q2f_cloze Everyone (f) hates me. 0 0 0 0 0 0 0 740 0 ▁▁▁▇▁▁▁▁
m5s1q2g_cloze The players want to beat (g) . 0 0 0 0 0 0 0 740 0 ▁▁▁▇▁▁▁▁
m5s1q2h_cloze
  1. Where do I have to go to school?
0 0 0 0 0 0 0 740 0 ▁▁▁▇▁▁▁▁
m5s1q2i_cloze Father: You are going and that is final. I will give you two (i) 0 0 0 0 0 0 0 740 0 ▁▁▁▇▁▁▁▁
m5s1q2j_cloze have to go to school today. First, you are 40 (j) years old. 0 0 0 0 0 0 0 740 0 ▁▁▁▇▁▁▁▁
m5s1q2k_cloze Javid, it is (a) half past seven. 0 0 0 0 0 0 0 740 0 ▁▁▁▇▁▁▁▁
m6sa1q1a NA 0.92 0.26 0 1 1 1 1 740 0 ▁▁▁▁▁▁▁▇
m6sa1q1b NA 0.83 0.37 0 1 1 1 1 740 0 ▂▁▁▁▁▁▁▇
m6sa1q1c NA 0.79 0.41 0 1 1 1 1 740 0 ▂▁▁▁▁▁▁▇
m6sa1q1d NA 0.93 0.26 0 1 1 1 1 740 0 ▁▁▁▁▁▁▁▇
Note:
Summary table shows unweighted summary statistics from teacher language assessment.
Table 18: Summary Statistics of Lao PDR Math Assessment Items for Teachers
Item Label Mean Std Dev Min 25th Percentile Median 75th Percentile Max # Complete Cases # Missing Cases Histogram
m5s2q10a_data 10a. Look at the graph. How far has Joe ridden after 6 hours? 0.33 0.47 0 0 0 1 1 740 0 ▇▁▁▁▁▁▁▃
m5s2q10b_data 10b. Chan started riding at 8.30 in the morning. How far had he gone at 12.00pm? 0.14 0.34 0 0 0 0 1 740 0 ▇▁▁▁▁▁▁▁
m5s2q11a_number 11a. √(144= )12 0.22 0.41 0 0 0 0 1 740 0 ▇▁▁▁▁▁▁▂
m5s2q11b_number 11b. 12.15-11.83= 0.32 0.29 0.46 0 0 0 1 1 740 0 ▇▁▁▁▁▁▁▃
m5s2q11c_number 11c. 3/4÷7/8= 21/32 0.12 0.32 0 0 0 0 1 740 0 ▇▁▁▁▁▁▁▁
m5s2q12_number
  1. What is n?
0.1 0.31 0 0 0 0 1 740 0 ▇▁▁▁▁▁▁▁
m5s2q13a_geometric 13a. (a) Perimeter: 0.073 0.26 0 0 0 0 1 740 0 ▇▁▁▁▁▁▁▁
m5s2q13b_geometric 13b. (b) Area: 90 cm2 0.17 0.38 0 0 0 0 1 740 0 ▇▁▁▁▁▁▁▂
m5s2q1c_number 1c. 343+215+127= 685 0.89 0.32 0 1 1 1 1 740 0 ▁▁▁▁▁▁▁▇
m5s2q1d_number 1d. 72÷9= 7 0.86 0.34 0 1 1 1 1 740 0 ▁▁▁▁▁▁▁▇
m5s2q1e_number 1e. 37×13 = 3711 0.84 0.37 0 1 1 1 1 740 0 ▂▁▁▁▁▁▁▇
m5s2q2_number
  1. Which two numbers add up to make 0.81?
0.64 0.48 0 0 1 1 1 740 0 ▅▁▁▁▁▁▁▇
m5s2q3_number
  1. Circle the one that gives the smallest answer?
0.77 0.42 0 1 1 1 1 740 0 ▂▁▁▁▁▁▁▇
m5s2q4a_number 4a. Complete these fractions so that they are equivalent 0.41 0.49 0 0 0 1 1 740 0 ▇▁▁▁▁▁▁▆
m5s2q4b_number 4b. Complete these fractions so that they are equivalent 0.37 0.48 0 0 0 1 1 740 0 ▇▁▁▁▁▁▁▅
m5s2q5_number
  1. 2 exercise books cost 14 Kips. What is the cost of 15 exercise books?
0.54 0.5 0 0 1 1 1 740 0 ▇▁▁▁▁▁▁▇
m5s2q6_geometric
  1. How many sides does a triangle have?
0.8 0.4 0 1 1 1 1 740 0 ▂▁▁▁▁▁▁▇
m5s2q7_geometric
  1. Lines that cannot meet are lines
0.59 0.49 0 0 1 1 1 740 0 ▆▁▁▁▁▁▁▇
m5s2q8_data
  1. What time did Chanla arrive?
0.43 0.5 0 0 0 1 1 740 0 ▇▁▁▁▁▁▁▆
m5s2q9a_data 9a. How many people had cats? 0.51 0.5 0 0 1 1 1 740 0 ▇▁▁▁▁▁▁▇
m5s2q9b_data 9b. Which animal was the least popular? 0.44 0.5 0 0 0 1 1 740 0 ▇▁▁▁▁▁▁▆
m6sa2q1a NA 0.97 0.18 0 1 1 1 1 740 0 ▁▁▁▁▁▁▁▇
m6sa2q1b NA 0.84 0.37 0 1 1 1 1 740 0 ▂▁▁▁▁▁▁▇
Note:
Summary table shows unweighted summary statistics from teacher math assessment.